Before conducting imputations, I excluded participants who said their sexual preferences were for “both” genders or the same gender (n = 76). I further excluded people who did not identify as black or coloured (n = 7) and people who did not report partners in the previous year (n = 170). Participants who had missing observations on those characteristics were left in the dataset. This left 1074 relationships reported by 647 participants. Of those relationships 400 started in the 12 months preceeding the survey. I imputed 50 datasets using the random forest method for continuous and nominal categorical variables and the “polr” method for our ordinal variables.


Figure 1. Age mixing pattern for randomly selected imputed dataset. Model 1 represents the linear mixed effects model with age as a linear term. Model 2 represents the GAMM with age as a smoothed term



Figure 2. 2A visualizes the spread of the residuals for the different models. Model 1 is the linear mixed effect model with age as a linear term, while Model 2 is a GAMM. 2b visualizes the pattern of residuals for the lme and gamm. In both models there appears to be constant variance



Figure 3. Extractions of model slopes, intercepts, intercept variance and residual variance for each imputed dataset



Figure 4. Fraction of relationships with different partner age groups, among those who are HIV positive



Figure 5. Age mixing pattern for those who are HIV positive



Figure 6. Distribution of bridge widths for each imputed dataset, by sex and HIV status



Figure 7. Model coefficients for relationship between HIV and bridge width. Results from negative binomial, generalized additive models with bridge width as the outcome. This is only among participants who reported more than 1 relationship in the previous year. Models adjust for race and age.



Figure 8. Expected bridge widths for different values of age (smooth term), by gender. Each line represents a different imputed dataset. These curves represent typical values of race (black) and hiv status (negative)



Figure 9. Effect of HIV on whether a participant had a concurrent relationship in the previous year, stratified by gender. Odds Ratios (ORs) are from generalized additive models. Models are adjusted for age (smooth term) and race.


## Warning: Transformation introduced infinite values in continuous y-axis
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Figure 10. Effect of HIV on whether a participant had a concurrent relationship in the previous year, stratified by gender. Odds Ratios (ORs) are from generalized additive models. Models are adjusted for bridgewidth, age (smooth term) and race.


## Warning: Transformation introduced infinite values in continuous y-axis
## Warning: Removed 11 rows containing missing values (geom_point).
## Warning: Removed 97 rows containing missing values (geom_pointrange).


Figure 11. Effect of bridgewidth on whether a participant had a concurrent relationship in the previous year, stratified by gender. Odds Ratios (ORs) are from generalized additive models. Models are adjusted for age (smooth term) and race.



Figure 12. Effect of bridgewidth on whether a participant had a concurrent relationship in the previous year, stratified by gender. Odds Ratios (ORs) are from generalized additive models. Models are adjusted for hiv, age (smooth term) and race.


## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 2 rows containing missing values (geom_pointrange).


Figure 13. Predicted probabilities of having had a concurrent relationship in the previous year for different values of age (smooth term), by gender. Each line represents a different imputed dataset. These curves represent typical values of race (black) and hiv status (negative)



Figure 14. Predicted probabilities of having had a concurrent relationship in the previous year for different values of age (smooth term), by gender. Each line represents a different imputed dataset. These curves represent typical values of race (black) and bridgewidth (3)



Figure 15. Predicted probabilities of having had a concurrent relationship in the previous year for different values of age (smooth term), by gender. Each line represents a different imputed dataset. These curves represent typical values of race (black), bridgewidth (3) and HIV status (Positive)



Figure 16. Effect of HIV on “Always” using a condom in relationship, stratified by gender. Odds Ratios (ORs) are from generalized additive mixed models with a random intercept for the participant. Models are adjusted for age and race.



Figure 17. Effect of HIV on “Always” using a condom in relationship, stratified by gender. Odds Ratios (ORs) are from generalized additive mixed models with a random intercept for the participant. Models are adjusted for bridgewidth, age and race.



Figure 18. Effect of bridgewidth on “Always” using a condom in relationship, stratified by gender. Odds Ratios (ORs) are from generalized additive mixed models with a random intercept for the participant. Models are adjusted for age (smooth term) and race.



Figure 19. Effect of bridgewidth on “Always” using a condom in relationship, stratified by gender. Odds Ratios (ORs) are from generalized additive mixed models with a random intercept for the participant. Models are adjusted for hiv status, age (smooth term) and race.



Figure 20. Predicted probabilities of “Always” using a condom in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models with a random intercept for the participant. Models are adjusted for hiv status and race.



Figure 21. Predicted probabilities of “Always” using a condom in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models with a random intercept for the participant. Models are adjusted for bridgewidth and race.



Figure 22. Predicted probabilities of “Always” using a condom in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models with a random intercept for the participant. Models are adjusted for bridgewidth, hiv status and race.



Figure 23. Distribution of average number of times sex occurred per week in relationships, stratified by gender and imputation dataset



Figure 24. Effect of HIV on average number of times sex occurred per week in the relationship, stratified by gender. Incidence Rate Ratios (IRRs) are from generalized additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for age and race.



Figure 25. Effect of HIV on average number of times sex occurred per week in the relationship, stratified by gender. Incidence Rate Ratios (IRRs) are from generalized additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for bridgewidth, age and race.



Figure 26. Effect of bridgewidth on average number of times sex occurred per week in the relationship, stratified by gender. Incidence Rate Ratios (IRRs) are from generalized additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for age and race.



Figure 27. Effect of bridgewidth on average number of times sex occurred per week in the relationship, stratified by gender. Incidence Rate Ratios (IRRs) are from generalized additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for hiv status, age and race.



Figure 28. Predicted average number of times sex occurred per week in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for hiv status and race.



Figure 29. Predicted average number of times sex occurred per week in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for bridgewidth and race.



Figure 30. Predicted average number of times sex occurred per week in a relationship for different ages of participant, stratified by gender. The predictions are from generalised additive mixed models (poisson outcome) with a random intercept for the participant. Models are adjusted for bridgewidth, hiv status, and race.